Study Of Physics
CH.5 Vectors
You have already studied in the third chapter about scalar and vector quantities. Scalars are those physical quantities which can be described completely by a number(magnitude) and a unit,such as mass, speed, time and volume etc. Whereas vectors are those quantities which need magnitude as well as direction to completely describe them, such as weight, velocity, acceleration and force etc.
Vectors play an important role in physics, velocity and acceleration of a moving object and forces acting on it are all described by vectors. Many other physical quantities can be usefully thought of as vectors. Although most of them do not represent distances (such as position or displacement), their magnitude and direction can be still represented by the length and direction of an arrow. The mathematical representation of a physical vector depends on the coordinate system used to describe it. Other vector-like objects that describe physical quantities and transform in a similar way under changes of the coordinate system.
Vectors play an important role in physics, velocity and acceleration of a moving object and forces acting on it are all described by vectors. Many other physical quantities can be usefully thought of as vectors. Although most of them do not represent distances (such as position or displacement), their magnitude and direction can be still represented by the length and direction of an arrow. The mathematical representation of a physical vector depends on the coordinate system used to describe it. Other vector-like objects that describe physical quantities and transform in a similar way under changes of the coordinate system.
Examples in one dimension
Since the physicist's concept of force has a direction and a magnitude, it may be seen as a vector. As an example, consider a rightward force F of 15 Newtons. If the positive axis is also directed rightward, then F is represented by the vector 15 N, and if positive points leftward, then the vector for F is −15 N. In either case, the magnitude of the vector is 15 N. Likewise, the vector representation of a displacement Δs of 4 meters to the right would be 4 m or −4 m, and its magnitude would be 4 m regardless.
In physics and engineering
Vectors are fundamental in the physical sciences. They can be used to represent any quantity that has both a magnitude and direction, such as velocity, the magnitude of which is speed. For example, the velocity 5 meters per second upward could be represented by the vector (0,5) (in 2 dimensions with the positive y axis as 'up'). Another quantity represented by a vector is force, since it has a magnitude and direction. Vectors also describe many other physical quantities, such as displacement, acceleration, momentum, and angular momentum. Other physical vectors, such as the electric and magnetic field, are represented as a system of vectors at each point of a physical space; that is, a vector field.
Since the physicist's concept of force has a direction and a magnitude, it may be seen as a vector. As an example, consider a rightward force F of 15 Newtons. If the positive axis is also directed rightward, then F is represented by the vector 15 N, and if positive points leftward, then the vector for F is −15 N. In either case, the magnitude of the vector is 15 N. Likewise, the vector representation of a displacement Δs of 4 meters to the right would be 4 m or −4 m, and its magnitude would be 4 m regardless.
In physics and engineering
Vectors are fundamental in the physical sciences. They can be used to represent any quantity that has both a magnitude and direction, such as velocity, the magnitude of which is speed. For example, the velocity 5 meters per second upward could be represented by the vector (0,5) (in 2 dimensions with the positive y axis as 'up'). Another quantity represented by a vector is force, since it has a magnitude and direction. Vectors also describe many other physical quantities, such as displacement, acceleration, momentum, and angular momentum. Other physical vectors, such as the electric and magnetic field, are represented as a system of vectors at each point of a physical space; that is, a vector field.
Ch.05: Vectors5.1 :- Vector Representation
5.2 :- Negative Vector
5.3 :- Addition of Vectors
5.4 :- Subtraction of Vectors
5.5 :- Multiplication by a Number
5.6 :- Trigonometric Ratios
5.7 :- Resolution of Vectors
5.2 :- Negative Vector
5.3 :- Addition of Vectors
5.4 :- Subtraction of Vectors
5.5 :- Multiplication by a Number
5.6 :- Trigonometric Ratios
5.7 :- Resolution of Vectors
Ch.06: Equilibrium
Ch.07: Circular Motion and Gravition
Ch.08: Work,Power And Energy
Ch.09: Simple Machines
Ch.10: Properties of Matter
Ch.11: Heat
Ch.07: Circular Motion and Gravition
Ch.08: Work,Power And Energy
Ch.09: Simple Machines
Ch.10: Properties of Matter
Ch.11: Heat
